Periodic versus Disordered Charge Sequences

The arguments of the previous section yield a straightforward proof of the convergence of F w]y toward F, when cu is a typical realization of the random charges u . 

Theorem 4.5 Under the same assumptions as in Theorem. 1, we have 

We use the chopping procedure used in proving Lemma 4.3 and Lemma 4.4. In fact a direct b5rproduct of the proofs of these two lemmas is that for every n 

T c (log(T) + ojjt ) for some c 0 that does not depend on the choice of 

The rightmost term in this formula vanishes P( dw)-a.s. and in as T tends to infinity. Therefore, by Theorem 4.1, the proof is complete.  

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